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Waiting Time Models of Cancer Progression

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  • MORITZ GERSTUNG
  • NIKO BEERENWINKEL

Abstract

Cancer progression is an evolutionary process driven by mutation and selection in a population of tumor cells. In multistage models of cancer progression, each stage is associated with the occurrence of genetic alterations and their fixation in the population. The accumulation of mutations is described using conjunctive Bayesian networks, an exponential family of waiting time models in which the occurrence of mutations is constrained by a partial temporal order. Two opposing limit cases arise if mutations either follow a linear order or occur independently. Exact analytical expressions for the waiting time until a specific number of mutations have accumulated are derived in these limit cases as well as for the general conjunctive Bayesian network. In a stochastic population genetics model that accounts for mutation and selection, waves of clonal expansions sweep through the population at equidistant intervals. An approximate analytical expression for the waiting time is compared to the results obtained with conjunctive Bayesian networks.

Suggested Citation

  • Moritz Gerstung & Niko Beerenwinkel, 2010. "Waiting Time Models of Cancer Progression," Mathematical Population Studies, Taylor & Francis Journals, vol. 17(3), pages 115-135.
    • Handle: RePEc:taf:mpopst:v:17:y:2010:i:3:p:115-135
    DOI: 10.1080/08898480.2010.490994
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    1. Timothy J. Ley & Elaine R. Mardis & Li Ding & Bob Fulton & Michael D. McLellan & Ken Chen & David Dooling & Brian H. Dunford-Shore & Sean McGrath & Matthew Hickenbotham & Lisa Cook & Rachel Abbott & D, 2008. "DNA sequencing of a cytogenetically normal acute myeloid leukaemia genome," Nature, Nature, vol. 456(7218), pages 66-72, November.
    2. N. Beerenwinkel & S. Sullivant, 2009. "Markov models for accumulating mutations," Biometrika, Biometrika Trust, vol. 96(3), pages 645-661.
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    Cited by:

    1. Urszula Foryś & Jan Poleszczuk & Ting Liu, 2014. "Logistic Tumor Growth with Delay and Impulsive Treatment," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(3), pages 146-158, September.
    2. Moritz Gerstung & Hani Nakhoul & Niko Beerenwinkel, 2011. "Evolutionary Games with Affine Fitness Functions: Applications to Cancer," Dynamic Games and Applications, Springer, vol. 1(3), pages 370-385, September.
    3. Michel Malo & Amandine Cartier-Michaud & Elisabeth Fabre-Guillevin & Guillaume Hutzler & Franck Delaplace & Georgia Barlovatz-Meimon & Annick Lesne, 2010. "When a Collective Outcome Triggers a Rare Individual Event: A Mode of Metastatic Process in a Cell Population," Mathematical Population Studies, Taylor & Francis Journals, vol. 17(3), pages 136-165.

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